Binary Image Analysis Segmentation produces homogenous regions - - PowerPoint PPT Presentation

E.G.M. Petrakis Binary Image Processing 1

Binary Image Analysis

• Segmentation produces homogenous

regions

– each region has uniform gray-level – each region is a binary image (0: background, 1: object or the reverse) – more intensity values for overlapping regions

• Binary images are easier to process and

analyze than gray level images

E.G.M. Petrakis Binary Image Processing 2

Binary Image Analysis Tasks

• Noise suppression
• Run-length encoding
• Component labeling
• Contour extraction
• Medial axis computation
• Thinning
• Filtering (morphological operations)
• Feature extraction (size, orientation etc.)

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Noise suppression

• Small regions are not useful information

– apply “size filter” to remove such regions – all regions below T pixels in size are removed by changing the value of their pixels to 0 (background) – it is generally difficult to find a good value of T – if T is small, some noise will remain – if T is large, useful information will be lost

E.G.M. Petrakis Binary Image Processing 4

• riginal

noisy image filtered Image T=10

• riginal

noisy image filtered image T=25 too high!

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Run-Length encoding

• Compact representation of a binary image
• Find the lengths of “runs” of 1 pixels sequences

E.G.M. Petrakis Binary Image Processing 6

Component Labeling

• Assign different labels to pixels belonging to

different regions (components)

– connected components – not necessary for images with one region

binary image labeled connected components

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Sequential Algorithm

1. Scan the image from left to right, top to bottom; if the pixel is 1 then a) if only one of the upper or left pixels has a label, copy this label to current pixel b) if both have the same label, copy this label c) if they have different labels, copy one label and mark these two labels as equivalent d) if there are no labeled neighbors, assign it a new label 2. Scan the labeled image and replace all equivalent labels with a common label 3. If there are no neighbors, go to 1

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Contour Extraction

• Find all 8-connected pixels of a region that are

adjacent to the background

– select a starting pixel and track the boundary until it comes back with the starting pixel

binary region boundary

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Boundary Following

• Scan the image from left to right and from

top to bottom until an 1 pixel is found

1) stop if this is the initial pixel 2) if it is 1, add it to the boundary 3) go to a 0 4-neighbor on its left 4) check the 8-neighbors of the current pixel and go to the first 1 pixel found in clockwise

• rder

5) go to step 2

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Area – Center

• Binary (or gray) region B[i,j]

– B[i,j] = 1 if (i,j) in the region, 0 otherwise – Area: – Center of gravity:

∑∑

= =

=

N i M j

j i B A

1 1

] , [

A j i jB x

N i M j

∑∑

= =

=

1 1

] , [

A j i iB y

N i M j

∑∑

= =

=

1 1

] , [

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Orientation

• Angle with the horizontal direction
• Find angle θ minimizing

] , [

1 1 2

j i B r E

N i M j ij

∑∑

= =

=

θ rij ρ = x cos θ + y sin θ x

y

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Computing Orientation

• E = a sin2 θ – b sin θ cos θ+c cos2θ, where

] , [ ] , [ ] , [

1 1 2 1 1 1 1 2

j i B y c j i B y x b j i B x a

N i M j ij ij N i M j ij N i M j ij

∑∑ ∑∑ ∑∑

= = = = = =

= = =

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Computation Orientation (cont.)

• From which we get
• Differentiating with respect to θ and setting the

result to zero

– tan2θ = b/(a-c) unless b = 0 and a = c

• Consequently
• The solution with the + minimizes E
• The solution with the – maximizes E

θ θ 2 sin 2 cos ) ( ) (

2 1 2 1 2 1

b c a c a E − − − + =

2 2 2 2

) ( 2 cos , ) ( 2 sin c a b c a c a b b − + − ± = − + ± = θ θ

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Computation Orientation (cont.)

• Compute Emin, Emax minimum and

maximum of the least second moment E

• The ratio e = Emax/Emin represents roundness

– e 0 for lines – e 1 for circles

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Distance Transform

• Compute the distance of each pixel (i,j)

from the background S

• at iteration n compute Fn[i,j]:
• F0[i,j] = f[i,j] (initial values)
• Fn[i,j] = F0[i,j] + min(Fn-1[u,v])
• (u,v) are the 4-neighbor pixels of (i,j) that is

pixels with D([i,j],[u,v]) = 1

• repeat until no distances changes

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Example of Distance Transform

• Distance transform of an image after the first and second

iterations

– on the first iteration, all pixels that are not adjacent to S are changed to 2 – on succeeding iterations only pixels further away from S change

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Skeleton (Medial Axis)

• Set of pixels with locally maximum distance from

the background S

• Take the distance transform and keep (i,j) Keep a

point (i,j) if it is the max in its 4-neighborhood:

D([i,j],S): locally maximum that is D([i,j],S) >= D([u,v],S) where (u,v) are the 4-neighbors of (i,j)

• The region can be reconstructed from its skeleton

– take all pixels within distance D(i,j) from each pixel (i,j) of the skeleton

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Examples of Medial Axis Transform

the medial axis transform is very sensitive to noise

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Thinning

• Binary regions are reduced to their center lines

– also called skeletons or core lines – suitable for elongated shapes and OCR – each region (e.g., character) is transformed to a line representation – further analysis and recognition is facilitated

• Iteratively check the 8-neighbors of each pixel

– delete pixels connected with S unless the 8-neighbor relationship with the remaining pixels is destroyed and except pixels at the end of a line – until no pixels change

E.G.M. Petrakis Binary Image Processing 20

no pixels change after 5 iterations

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Filtering Operations

• Expansion: some background pixels adjacent to

the region are changed from 0 to 1

– the region is expanded – fills gaps, the region is smoothed

• Shrinking: some pixels are changed from 1 to 0

– the region is shrinked – removes noise, thinning

• A combination of Expansion with Shrinking may

achieve better smoothing

E.G.M. Petrakis Binary Image Processing 22

noisy image expanding followed by shrinking filled holes but did not eliminate noise shrinking followed by expanding eliminated noise but did not fill the holes

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Morphological Filtering

• Image filtering using 4 filtering operations

– two basic: Dilation, Erosion plus – two derived: Opening, Closing – and a Structuring Element (SE) whose size and shape may vary

SE: rectangle with R=1,2,3 SE: circle with R=1,2,3

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Erosion - Dilation

• Erosion: apply the SE on every pixel (i,j) of the

image f

– (i,j) is the center of the SE – if the whole SE is included in the region then, f[i,j] = 1 – otherwise, f[i,j] = 0 – erosion shrinks the object

• Dilation: if at least one pixel of the SE is inside

the region f[i,j] = 1

– dilation expands the region

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• riginal image

Structuring Element (SE) Erosion with the SE at various positions

• f the original image

E.G.M. Petrakis Binary Image Processing 26

the erosion of the original image with the SE the bold line shows the border

• f the original image

the dilation of the original image with the SE the bold line shows the border

• f the original image

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Opening - Closing

• Opening: erosion followed by dilation with

the same SE

– filters out “positive” detail, shirks the region

• Closing: dilation followed by erosion with

the same SE

– smoothes by expansion, fills gaps and holes smaller than the SE

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initial erosion initial dilation succeeding dilation succeeding erosion

• pening

closing

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Pattern Spectrum

• Succeeding Openings with the same SE
• Succeeding Closings with the same SE

i=0 i=-1 i=-2 i=-3 i=-4 i=0 i=1 i=2 i=3 i=4

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Example of Pattern Spectrum

• Size vector p=(a-n,a-n+1,a-n+2,….a, a1, a2, a3, …, an)
• Distance between shapes A,B:
• pening
• riginal

closing

• 4 -3 -2
• 1

1 2 3 4

2 / 1 2

) ( ) , ( ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = ∑

− = n n i i i

b a B A D